Examine how types of statistical variability recommended in GAISE can be taught alongside the data displays recommended in CCSSM.
Randall E. Groth
Randall E. Groth and Anna E. Bargagliotti
Two recent sets of guidelines that intersect statistics and complement each other can be used to plot an orderly progression of study.
Jennifer A. Bergner and Randall E. Groth
Part of the beauty of mathematics is that seemingly isolated branches of the subject can often be used together to produce solutions to problems. High school students need to engage in activities that help them see how the various branches of mathematics work together in problem-solving situations. NCTM (2000) underscores the importance of such activities, stating, “When students can see the connections across different mathematical content areas, they develop a view of mathematics as an integrated whole” (NCTM 2000, p. 354).
Randall E. Groth, Matthew Jones and Mary Knaub
Learning to work with bivariate data, a key goal of middle-grades statistics curricula, is aided by a sequence of lessons.
Randall E. Groth, Kristen D. Kent and Ebony D. Hitch
Students travel through a series of lessons as they analyze data and unpack the meaning of measures of center.
Randall E. Groth and Nancy N. Powell
Statistics plays a key role in shaping policy in a democratic society, so statistical literacy is essential for all citizens to keep a democratic government strong (Wallman 1993). However, fostering the statistical thinking is a complex endeavor. We ultimately need to engage students in all phases of the investigative cycle of statistics, including data gathering, data analysis, and inference.
Randall E. Groth and Jennifer A. Bergner
Conversations with colleagues can be valuable in thinking through the logistics of implementing the NCTM's (2000) recommendations for teaching mathematics.
Randall E. Groth, Jennifer A. Bergner and Jathan W. Austin
Normative discourse about probability requires shared meanings for disciplinary vocabulary. Previous research indicates that students’ meanings for probability vocabulary often differ from those of mathematicians, creating a need to attend to developing students’ use of language. Current standards documents conflict in their recommendations about how this should occur. In the present study, we conducted microgenetic research to examine the vocabulary use of four students before, during, and after lessons from a cycle of design-based research attending to probability vocabulary. In characterizing students’ normative and nonnormative uses of language, we draw implications for the design of curriculum, standards, and further research. Specifically, we illustrate the importance of attending to incrementality, multidimensionality, polysemy, interrelatedness, and heterogeneity to foster students’ probability vocabulary development.
Randall E. Groth and Claudia R. Burgess
Online conversations help teachers engage in constructive criticism and attend more carefully to aligning lesson plans with problem solving.
Randall E. Groth, Jennifer A. Bergner, Jathan W. Austin, Claudia R. Burgess and Veera Holdai
Undergraduate research is increasingly prevalent in many fields of study, but it is not yet widespread in mathematics education. We argue that expanding undergraduate research opportunities in mathematics education would be beneficial to the field. Such opportunities can be impactful as either extracurricular or course-embedded experiences. To help readers envision directions for undergraduate research experiences in mathematics education with prospective teachers, we describe a model built on a design-based research paradigm. The model engages pairs of prospective teachers in working with faculty mentors to design instructional sequences and test the extent to which they support children’s learning. Undergraduates learn about the nature of systematic mathematics education research and how careful analyses of classroom data can guide practice. Mentors gain opportunities to pursue their personal research interests while guiding undergraduate pairs. We explain how implementing the core cycle of the model, whether on a small or large scale, can help teachers make instructional decisions that are based on rich, qualitative classroom data.